On characterization of simple orthogonal groups of odd dimension in the class of periodic groups

Suppose that $n$ is an integer, $n\geq 3$. We prove that a periodic group saturated with a set of the finite simple groups $O_{2n+1}(q)$, where $q$ is congruent to $\pm3$ modulo $8$, is isomorphic to $O_{2n+1}(F)$ for some locally finite field $F$.